On formulaes of integration by parts for special type of power functions (in Ukrainian) |
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| Author |
ol_buhrii@i.ua
Ivan Franko National University of Lviv
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| Abstract |
We investigate properties of the function $\psi_{\alpha}(u)$,
where $\alpha>0$,
$u\in C^{m}(\overline{G})$ or $u\in W^{m,p}(G)$, $G\subset R^N$,
$\psi_{\alpha}$ is some power function,
for example, $\psi_{\alpha}(s)=|s|^{\alpha-1}s$.
In particular, some formulaes of integration by parts and differentiation
for observed functions are proved.
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| Keywords |
integration by parts formulae; differentiation formulae; exponential functions
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| DOI |
doi:10.15330/ms.45.2.118-131
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| Reference |
1. Metafune G., Spina C. An integration by part formula in Sobolev spaces// Mediterr. J. Math. – 2008. –
V.5. – P. 357–369.
2. Lions J.-L., Strauss W.A. Some non-linear evolution equations// Bulletin de la S. M. F. – 1965. – V.93. – P. 43–96. 3. Gajewski H., Groger K., Zacharias K. Nichtlineare operatorgleichungen und operatordifferentialgleichungen. – Moscow, 1978, 336 p. (in Russian) 4. Ladyzenskaya O.A., Uraltseva N.N. Linear and quasilinear elliptic equations. – Moscow, 1973, 576 p. (in Russian) 5. Kinderlehrer D., Stampacchia G. An introduction to variational inequalities and their applications – Moscow, 1983, 256 p. (in Russian) 6. Baiocchi C., Capelo A. Variational and quasivariational inequalities. Applications to free boundary problems. – Moscow, 1988, 448 p. (in Russian) 7. Kolmogorov A.N., Fomin S.V. Theory of functions and functional analysis. – Moscow, 1972, 496 p. (in Russian) 8. Bystrom J. Sharp constants for some inequalities connected to the p-Laplace operator// Jour. of Ineq. in Pure and Appl. Math. – 2005. – V.6, Issue2. – Article 56. 9. Gorodetskyi V.V., Nagnybida N.I., Nastasiev P.P. Methods of solving of function analysis problems. – Kyiv, 1990, 479 p. (in Russian) |
| Pages |
118-131
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| Volume |
45
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| Issue |
2
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| Year |
2016
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| Journal |
Matematychni Studii
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